Depends on how you define "efficiency". Are you looking for a more leisurely route? Do you have the time to go a bit further out of the way in order to avoid Chicagoland?
Not a fan of driving through any part of the Greater Chicago area. If it were me, I'd take I-39 south to US 24 east all the way across Indiana to Fort Wayne, I-469 around Fort Wayne and then pick up US 24 again to I-90 and on to Sandusky.
While I've not done this route as a continuous trip, I've done most of this in segments, from point A to point B. US 24, for me, was a good alternative to avoiding both Chicago and Indy. Only portion I've not done is in Ohio, but I suspect it's not a lot different from the Indiana portion.
